Hi-LOAM: Hierarchical Implicit Neural Fields for LiDAR Odometry and Mapping

Zhiliu Yang; Jianyuan Zhang; Lianhui Zhao; Jinyu Dai; Zhu Yang

cs.ROApr 2, 2026

Hi-LOAM: Hierarchical Implicit Neural Fields for LiDAR Odometry and Mapping

Authors: Zhiliu Yang, Jianyuan Zhang, Lianhui Zhao, Jinyu Dai, Zhu Yang

Organizations: School of Information Science and Engineering, Yunnan University, Kunming, Yunnan 650500, China. · Yunnan Key Laboratory of Intelligent Systems and Computing, Yunnan University, Kunming, Yunnan 650500, China. · School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China.

Abstract

LiDAR Odometry and Mapping (LOAM) is a pivotal technique for embodied-AI applications such as autonomous driving and robot navigation. Most existing LOAM frameworks are either contingent on the supervision signal, or lack of the reconstruction fidelity, which are deficient in depicting details of large-scale complex scenes. To overcome these limitations, we propose a multi-scale implicit neural localization and mapping framework using LiDAR sensor, called Hi-LOAM. Hi-LOAM receives LiDAR point cloud as the input data modality, learns and stores hierarchical latent features in multiple levels of hash tables based on an octree structure, then these multi-scale latent features are decoded into signed distance value through shallow Multilayer Perceptrons (MLPs) in the mapping procedure. For pose estimation procedure, we rely on a correspondence-free, scan-to-implicit matching paradigm to estimate optimal pose and register current scan into the submap. The entire training process is conducted in a self-supervised manner, which waives the model pre-training and manifests its generalizability when applied to diverse environments. Extensive experiments on multiple real-world and synthetic datasets demonstrate the superior performance, in terms of the effectiveness and generalization capabilities, of our Hi-LOAM compared to existing state-of-the-art methods.

Figures & tables

Fig. 1 : Reconstructed map and estimated trajectory generated via our implicit Hi-LOAM. The above case is evaluated on the sequence 07 of KITTI dataset, superior mapping quality and accurate poses are obtained via deep utilization of hierarchical neural features.

Fig. 2 : The Overview of Our Hi-LOAM Framework . The main data stream is depicted as following. Sampled points $\mathbf{P}_{\mathrm{C}_{t}}$ along the ray is used to construct neural signed distance fields (nSDF) based on the octree. For the first two scans, poses $\mathbf{P}_{0}$ and $\mathbf{P}_{1}$ are predefined and nSDF are created. For following scans, original points $\mathbf{P}_{t}$ are firstly matched with octree of sub map to estimate the pose $\mathbf{T}_{\mathrm{WC}_{t}}^{*}$ . Then, $\mathbf{P}_{t}$ is transformed into the global coordinate system via $\mathbf{T}_{\mathrm{WC}_{t}}^{*}$ , $\mathbf{P}_{\mathrm{W}_{t}}$ is registered to expand the nSDF, this process is repeated in turn. The separate optimization strategies are designed for odometry and mapping, the trainable parameters and frozen parameters are marked correspondingly.

Fig. 3 : The correspondence among the three tables in certain level of octree. The eight corners of a node correspond to eight features stored in table $\mathbf{F}$ . The hierarchical nodes and their corresponding corners are stored in Morton code form in tables $\mathbf{N}$ and $\mathbf{G}$ .

Method	Type	00	01	02	03	04	05	06	07	08	09	10	Avg.
LeGO-LOAM [ 26 ]	feature points	2.17	13.4	2.17	2.34	1.27	1.28	1.06	1.12	1.99	1.97	2.21	2.49
F-LOAM [ 64 ]	feature points	0.78	1.43	0.92	0.86	0.71	0.57	0.65	0.63	1.12	0.77	0.79	0.84
MULLS [ 43 ]	feature points	0.56	0.64	0.55	0.71	0.41	0.30	0.30	0.38	0.78	0.48	0.59	0.52
VG-ICP [ 65 ]	dense points	2.16	2.38	0.99	0.67	0.55	0.45	0.24	0.99	1.74	0.95	0.95	1.10
CT-ICP [ 27 ]	dense points	0.49	0.76	0.52	0.72	0.39	0.25	0.27	0.31	0.81	0.49	0.48	0.50
KISS-ICP [ 19 ]	dense points	0.52	0.63	0.51	0.66	0.36	0.31	0.26	0.33	0.82	0.51	0.56	0.50

TABLE I : Comparison of Average Relative Translational Drifting Error (%) on KITTI Odommetry Benchmark. The best results are highlighted in bold, and the second-best results are underlined. “-” indicates the result is not reported in the related paper, ‘-LO’ in the name of methods indicates that only the odometry component of the method is used for evaluation. And the definition of those symbols are applicable to other tables in the rest of the paper. Consistent with other methods, we use the average relative translational error in % as the metric for evaluating odometry drift.

Method	Type	00	01	02	03	04	05	06	07	08	09	10	Avg.
LeGO-LOAM [ 26 ]	feature points	2.3	19.7	5.3	1.6	0.4	1.2	1.0	1.5	5.9	2.0	1.7	5.3
F-LOAM [ 64 ]	feature points	5.0	3.2	8.6	0.7	0.3	3.4	0.5	0.6	3.1	1.6	1.2	2.6
KISS-ICP [ 19 ]	dense points	5.7	30.7	17.8	3.4	1.1	1.9	0.9	0.8	4.8	3.7	2.3	6.6
SuMa [ 30 ]	surfels	2.9	13.8	8.4	0.9	0.4	1.2	0.4	0.5	2.8	2.9	1.3	3.2
Litamin [ 66 ]	normal distribution	5.8	15.9	10.7	0.8	0.7	2.4	0.9	0.6	2.5	2.1	1.0	3.9
Puma [ 44 ]	mesh	6.6	32.6	18.5	2.2	0.9	3.3	2.4	0.9	6.3	3.9	4.4	7.5

TABLE II : Comparison of Absolute Trajectory Error (m) on KITTI Odometry Benchmark.

Method	KA1	KA2	KA3	DC1	DC2	DC3	RS1	RS2	RS3	Avg.
F-LOAM [ 64 ]	49.16	35.93	38.36	36.89	26.72	31.97	91.85	104.25	119.79	59.44
KISS-ICP [ 19 ]	20.81	13.52	14.85	20.26	12.79	13.17	14.35	32.74	75.14	24.18
SuMa [ 30 ]	10.45	9.33	10.33	13.00	86.04	12.03	114.89	818.74	367.41	160.25
MULLS [ 43 ]	19.72	15.26	6.93	14.95	11.31	6.00	41.25	45.05	44.18	22.74
PIN-LO [ 17 ]	29.07	24.74	23.05	22.07	12.94	23.42	45.81	54.41	44.41	31.10
Hi-LOAM	18.73	20.80	25.98	20.20	16.38	15.42	42.36	52.14	38.95	27.88

TABLE III : Localization Performance Comparison (ATE RMSE [m]) on MulRAN LiDAR Dataset.

Fig. 4 : The Qualitative Results of Odometry Comparison on Sequence 00 of KITTI Dataset. The left side displays trajectories comparison of different methods. The right side compares errors along the X, Y, and Z axes among our method and other methods. The black dashed line represents the ground truth trajectory. ( Best viewed with zoom-in. )

Method	00	01	02	03	04	05	Avg.
SLAMesh [ 59 ]	0.28	0.56	0.28	0.29	0.38	0.33	0.35
MULLS [ 43 ]	0.38	0.55	0.26	0.35	0.38	0.43	0.39
PIN-SLAM [ 17 ]	0.25	0.39	0.19	0.26	0.24	0.27	0.27
Hi-LOAM	0.27	0.29	0.22	0.25	0.23	0.23	0.25

TABLE IV : Localization Performance Comparison (ATE RMSE [m]) on SemanticPOSS LiDAR Dataset.

Panel of Figure 9 — Fig. 5 : The Qualitative Results of Our Odometry on MulRAN Dataset. The black dashed line represents the ground truth, while the blue solid line represents our trajectory. ( Best viewed with zoom-in. )

Method	rpg	lab	base1	base4	cons2	camp2	Avg.
F-LOAM [ 64 ]	2.78	0.18	0.91	0.29	11.52	8.95	4.10
KISS-ICP [ 19 ]	0.22	0.07	0.32	0.11	0.84	1.98	0.58
HDLGraph-SLAM [ 75 ]	0.35	0.05	0.28	0.37	0.74	0.35	0.36
SLAMesh [ 59 ]	0.17	0.05	0.18	0.33	0.34	0.65	0.29
SuMa [ 30 ]	0.26	0.05	2.24	0.29	1.64	-	0.90
PIN-SLAM [ 17 ]	0.21	0.04	0.30	0.08	0.41	0.11	0.19

TABLE V : Localization Performance Comparison (ATE RMSE [m]) on Hilti-21 LiDAR Dataset.

Method	01	02	quad_e	math_e	ug_e	cloister	stairs	Avg.
F-LOAM [ 64 ]	6.74	✗	0.40	0.26	0.09	7.69	✗	3.04
KISS-ICP [ 19 ]	0.62	1.88	0.10	0.07	0.33	0.30	✗	0.55
SuMa [ 30 ]	2.03	3.65	0.28	0.16	0.09	0.20	1.85	1.18
MULLS [ 43 ]	2.51	8.39	0.12	0.35	0.86	0.41	✗	2.11
MD-SLAM [ 76 ]	-	1.74	0.25	-	-	0.36	0.34	-
SC-LeGO-LOAM [ 26 ]	-	1.30	0.09	-	-	0.20	3.20	-

TABLE VI : Localization Performance Comparison (ATE RMSE [m]) on Newer College LiDAR Dataset. ✗ denotes the execution failure.

Approach	Sensor	MaiCity 01
SuMa [ 30 ]	Velodyne HDL-64	6.1
F-LOAM [ 64 ]		6.2
KISS-ICP [ 19 ]		✗
Puma [ 44 ]		5.8
SLAMesh [ 59 ]		1.7
Mesh-LOAM [ 60 ]		1.6

TABLE VII : Localization Performance Comparison (ATE RMSE [cm]) on the Sequence 01 of MaiCity Dataset. ✗ denotes the execution failure.

Method	Pose	Quad from Newer College				Mai City
Method	Pose	Map. Acc. $\downarrow$	Map. Comp. $\downarrow$	C-l1. $\downarrow$	F-score (20cm) $\uparrow$	Map. Acc. $\downarrow$	Map. Comp. $\downarrow$	C-l1. $\downarrow$	F-score (10cm) $\uparrow$
VDB-Fusion [ 12 ]	KISS-ICP [ 19 ]	14.03	25.46	19.75	69.50	15.21	28.66	21.94	63.35
SHINE [ 24 ]	KISS-ICP [ 19 ]	14.87	20.02	17.45	68.85	14.46	34.03	24.24	64.38
Puma [ 44 ]	Own Odometry	15.30	71.91	43.60	57.27	7.89	9.14	8.51	68.04
SLAMesh [ 59 ]		19.21	48.83	34.02	45.24	5.67	12.99	9.33	75.10
NeRF-LOAM [ 16 ]		12.89	22.21	17.55	74.37	5.69	11.23	8.46	77.23

TABLE VIII : The 3D Reconstruction Accuracy of Different Methods on Newer College and Mai City Datasets.

Panel of Figure 14 — Fig. 6 : The Visualization of Our 3D Reconstruction Results on Mai City Dataset via Comparing with Other Related Methods. The mapping results in first row are original reconstruction result, and the second row presents the error maps with ground truth mesh as a reference, where the red points stand for large error above 25cm. ( Best viewed with zoom in. )

Panel of Figure 15 — Fig. 7 : The Visualization of Our 3D Reconstruction Results on Newer College Dataset via Comparing with Other Related Methods. The mapping results in first row are original reconstruction result, and the second row presents the error maps with using ground truth mesh as a reference, where the red points mean larger error up to 50 cm. ( Best viewed with zoom in.)

Fig. 8 : The Reconstructed Mesh of Our Hi-LOAM on Newer College Dataset. We show the estimated trajectory by overlapping it on the map for the sequence of the underground, and we show the inner structure for the sequence of stairs. ( Best viewed with zoom in. )

Fig. 9 : The Qualitative Results of Our Reconstructed Mesh on KITTI Dataset. Our reconstructed mesh on sequence 00, 04, 06, and 08 demonstrate the construction capacity of Hi-LOAM in large-scale environment.

Fig. 10 : The Reconstructed Mesh of our Hi-LOAM on Hilti-21 and Hilti-23 Datasets. The mapping environment of Hilti-23 is made up by construction sites, which are full with highly-repetitive or feature-less walls. The mapping ability for this extreme condition is shown in the above sub-figures. The estimated trajectory is also overlapped in the map to visualize the localization result. ( Best viewed with zoomin. )

LOF	KITTI							SemanticPOSS
LOF	00	02	04	06	08	10	Avg.	00	01	02	03	04	05	Avg.
1	5.96	10.42	0.45	0.76	2.93	0.88	3.57	0.28	0.43	0.21	0.29	0.25	0.29	0.29
2	5.00	11.35	0.17	0.66	2.93	0.88	3.50	0.27	0.41	0.20	0.28	0.22	0.24	0.27
3	5.00	8.60	0.14	0.63	2.80	0.81	3.00	0.27	0.29	0.22	0.25	0.23	0.23	0.25

TABLE IX : The Ablation Study of the Level of Feature (LOF) on KITTI and SemanticPOSS LiDAR Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation.

Fig. 11 : Ablation Study of Different Optimizer Setting. The blue line represents the results obtained by replacing the Levenberg-Marquardt (LM) method with the Adam optimizer in our approach. The black dashed line represents the ground truth trajectory. It is evaluated by first 380 scans in KITTI 06 , which is a typical case for optimizer selection.

Leaf Node Size	KITTI 03	KITTI 05	KITTI 06	KITTI 04	quad_e	ug_e	stairs	MaiCity 01	Avg.
Leaf Node Size	25m $\times$ 400m	10m $\times$ 400m	8m $\times$ 15m	5m $\times$ 8m	40m $\times$ 30m	30m $\times$ 20m	10m $\times$ 2m	100m $\times$ 5m
0.1	✗	2.097552	0.728338	0.155302	0.111781	4.796704	0.112531	0.016174	1.145483
0.2	✗	1.636037	0.529766	0.134920	0.093267	0.052786	0.077359	0.006776	0.360590
0.25	0.477824	1.460346	0.391477	0.154256	0.097045	0.076913	0.265139	0.014541	0.367193
0.3	0.544378	1.547646	0.521631	0.170558	0.099131	✗	0.261116	0.013292	0.451107

TABLE X : Sensitivity Analysis of Leaf Node Sizes on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.

Tree Levels	KITTI 03	KITTI 05	KITTI 06	KITTI 04	quad_e	ug_e	stairs	MaiCity 01
Tree Levels	25m $\times$ 400m	10m $\times$ 400m	8m $\times$ 15m	5m $\times$ 8m	40m $\times$ 30m	30m $\times$ 20m	10m $\times$ 2m	100m $\times$ 5m
9	✗	✗	✗	✗	0.100113	0.052786	0.169223	0.012432
10	✗	✗	✗	✗	0.097937	0.081195	0.079966	0.006776
11	82.758527	✗	0.761584	44.536743	0.099720	0.230535	0.112515	0.009499
12	0.477824	1.621471	0.488580	0.142222	0.104466	0.214824	0.138130	0.010439
13	0.572033	1.653113	0.391477	0.134920	0.100589	0.464130	0.194548	0.016236

TABLE XI : Sensitivity Analysis of Tree Level Numbers on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.

Submap Numbers	KITTI 03	KITTI 05	KITTI 06	KITTI 04	quad_e	ug_e	stairs	MaiCity 01
Submap Numbers	25m $\times$ 400m	10m $\times$ 400m	8m $\times$ 15m	5m $\times$ 8m	40m $\times$ 30m	30m $\times$ 20m	10m $\times$ 2m	100m $\times$ 5m
50	✗	✗	✗	✗	0.093394	0.052786	0.077359	0.006267
60	✗	✗	✗	✗	0.093809	0.068807	0.089445	0.012224
100	0.538114	1.564616	0.513978	0.150586	0.093267	0.081796	0.079966	0.012838
150	0.582111	1.717656	0.486967	0.145847	0.094171	0.069654	0.106437	✗
200	0.581955	1.460346	0.391477	0.134920	0.099720	0.134966	0.143389	✗

TABLE XII : Sensitivity Analysis of Submap Numbers on KITTI , Newer College , and Mai City Benchmark. Localization Performance (ATE RMSE [m]) are reported for system evaluation. ✗ denotes the execution failure.

Method	KITTI 00	KITTI 05	KITTI 08	NCD 02
Raw point cloud	13624.2	8284.7	12214.1	26559.0
SuMa [ 30 ]	887.7	512.6	835.7	79.0
Puma [ 44 ]	2032.9	1317.4	1894.1	1503.7
VDB Fusion [ 12 ]	748.1	434.6	958.6	462.5
PIN-SLAM [ 17 ]	102.1	66.3	138.8	76.8
Hi-LOAM	242.1	169.5	284.3	176.6

TABLE XIII : Memory consumption comparison with different method in MB. NCD means Newer College dataset.

Method	Time per frame [s] $\downarrow$	FPS [Hz] $\uparrow$	ARTE [%] $\downarrow$
PIN-SLAM [ 17 ]	0.034	29.4	0.51
NeRF-LOAM [ 16 ]	4.53	0.2	1.69
Hi-LOAM	0.6	1.7	0.48

TABLE XIV : Comparison of the average running time and the localization error of different method on KITTI sequence 00-10. ARTE represents the average relative translational error.

Submodule	KITTI 03	MaiCity 01	Quad_e	KA1	Lab	POSS 00
Odometry	0.3	0.14	0.34	0.38	0.2	0.49
Map Optimization	3.6	2.87	3.0	5.5	4.7	4.5

TABLE XV : Breakdown of Average Running Time per Frame (s) for Each Module on Different Datasets. Quad_e from the Newer College dataset, KAI from the MulRAN dataset, Lab from the Hilti-21 dataset, POSS 00 from the SemanticPOSS dataset.

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LIN-SLAM: Lightweight LiDAR--Inertial Neural SLAM for Real-Time Onboard Navigation

Shiqi Che, Yijie Liu, Shuo Wang, Wenxin Liu

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

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Geometric light detection and ranging (LiDAR)--inertial simultaneous localization and mapping (SLAM) provides efficient state estimation but lacks the continuous map representation and global refinement capabilities of neural implicit SLAM, while neural implicit methods remain computationally expensive. We propose Lightweight LiDAR--Inertial Neural SLAM (LIN-SLAM), a hybrid method that couples high-rate geometric LiDAR--inertial estimation with neural implicit tracking, continual mapping, and global refinement for accurate real-time onboard SLAM. Experiments on twelve representative sequences from three datasets spanning 32-, 64-, and 128-channel LiDAR configurations show that LIN-SLAM achieves the lowest overall mean absolute trajectory error (ATE) among the evaluated state-of-the-art geometric and neural implicit methods, while substantially reducing runtime compared with existing neural implicit SLAM methods. On a Unitree Go2 equipped with an NVIDIA Jetson Orin NX and a 16-channel LiDAR, LIN-SLAM sustains real-time localization and neural mapping over a 1.47-km indoor trajectory through challenging repetitive corridor environments, with an endpoint closure error of only 0.141~m. To the best of our knowledge, LIN-SLAM is the first LiDAR--inertial SLAM system with a neural implicit backend to achieve real-time online operation on a mobile robotic platform while maintaining state-of-the-art localization accuracy. The code will be released upon acceptance.

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